Our results give hints on how to summarize complex data sets best so that they remain actionable. Moreover, as the construction of surrogate data is a stochastic process, each of the procedures discussed here yields an ensemble of surrogate data with similar statistical properties. This highlights an interesting potential application of our results. Indeed, collecting data sets is an expensive task, and several data properties depend on context, making modeling of realistic temporal networks a problematic task. Simultaneously, the availability of data with real properties is crucial to inform data-driven models of diffusion processes such as epidemics of infectious diseases. Moreover, collected data typically have a limited duration, and merely repeating the data might create undesired biases [1]}. The various procedures we have described here make it possible to create synthetic surrogate data with properties very similar to empirical data without modeling assumptions. By tuning the backbone size, and hence the amount of surrogate data needed to be added to it, one can moreover tune the similarity between the original data and the surrogate replicas.
